Determine Which of the Following Are Trigonometric Identities $\csc ( \theta ) \sec ( \theta ) = \tan ( \theta )$

question 33

Multiple Choice

Determine which of the following are trigonometric identities.
I. $\csc ( \theta ) \sec ( \theta ) = \tan ( \theta )$
II. $\csc ( \theta ) \tan ( \theta ) = \sec ( \theta )$
III. $\tan ( \theta ) \sec ( \theta ) = \csc ( \theta )$
IV. $\csc ( \theta ) \sin ( \theta ) = 1$

• A) II is the only identity.
• B) II and IV are the only identities.
• C) I, III, and IV are the only identities.
• D) I is the only identity.
• E) II, III, and IV are the only identities.

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Definitions:

Strike-Slip Fault

A type of fault in which two blocks of the Earth's crust slide past each other horizontally along the fault plane.

Reverse Fault

A type of fault where the hanging wall moves up relative to the footwall, often created by compressive forces.

Normal Fault

A type of fault where the hanging wall has moved downward relative to the footwall, typically associated with extensional tectonics.

Horizontal Compression

A stress regime where forces push inwards from opposite sides, often leading to folding, faulting, or shortening of the Earth's crust.